Problem: You are given N items.
The value of the i-th item (1 \leq i \leq N) is v_i.
Your have to select at least A and at most B of these items.
Under this condition, find the maximum possible arithmetic mean of the values of selected items.
Additionally, find the number of ways to select items so that the mean of the values of selected items is maximized.

Constraints

* 1 \leq N \leq 50
* 1 \leq A,B \leq N
* 1 \leq v_i \leq 10^{15}
* Each v_i is an integer.

Input

The input is given from Standard Input in the following format:


N A B
v_1
v_2
...
v_N


Output

Print two lines.
The first line should contain the maximum possible arithmetic mean of the values of selected items. The output should be considered correct if the absolute or relative error is at most 10^{-6}.
The second line should contain the number of ways to select items so that the mean of the values of selected items is maximized.

Examples

Input

5 2 2
1 2 3 4 5


Output

4.500000
1


Input

4 2 3
10 20 10 10


Output

15.000000
3


Input

5 1 5
1000000000000000 999999999999999 999999999999998 999999999999997 999999999999996


Output

1000000000000000.000000
1

Solution (in CPP):

Solution:

#include<cstdio>
#include<cmath>
#include<algorithm>
#define ll long long

using namespace std;

ll v[55];
ll ans=0;//必须开long long，否则在极限情况下会数据超限
void cnt(int a,int b){
	double sum=1;
	if(a>b/2)	
		a=b-a;
	for(int i=b,j=1;i>=b-a+1;i--,j++){
		sum*=i*1.0/j;
	}
	ans+=sum;	
}

bool cmp(ll a,ll b){
	return a>b;//从大到小排序 
}

int main(){
	int n,min_,max_;
	scanf("%d %d %d",&n,&min_,&max_);
	for(int i=1;i<=n;i++){
		scanf("%lld",&v[i]);
	}
	
	sort(v+1,v+n+1,cmp);
	int num=min_;
	double ave=0;
	ave+=v[1];
	int same=1,dsam;
	for(int i=2;i<=min_;i++){
		ave+=v[i];
		if(v[i]==v[i-1]){
			same++;
		}
		else {
			same=1;
		}
	}
	ave/=num;//计算选最少的数时最大平均值
	dsam=min_-same;//已选择的不同的数 

	for(int i=min_+1;v[i]==v[min_]&&i<=n;i++){
		same++;//已选择+未选择的相同的数 
	} 
	if(dsam==0){//如果所有的数都相同 
		for(int k=min_;k<=max_;k++){
			if(k>same)	
				break;
			cnt(k,same);
		}
	}
	else {
		cnt(min_-dsam,same);
	}
	printf("%.6lf\n%lld\n",ave,ans);
	return 0; 
}